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Surname Koster (Koster , Custor , Costre ) , across the world, is a common cognomen. The last name Koster is characteristic of Netherlands, where it is quite a common surname, New Zealand, and Suriname (explore the name in all countries). Not in comparison with a country's population, it is commonest in Netherlands, the United States, and Germany. Very seldom, Koster is the forename as well as the last name.